High beta output stage for high speed operational amplifier

ABSTRACT

The present invention provides an high beta, high speed operational amplifier output stage ( 100 ). The advantages of the operational amplifier output stage over conventional methods disclosed is up to β 2  rather than a single beta. The present invention achieves this using an pre-driver sub-stage ( 122 ) having a plurality of translinear loops so that there is no net signal loss to the final sub-stage ( 123 ). The output of the disclosed operational amplifier output stage takes the form: 
     
       
         δI o ≈β n *β p *δI in . 
       
     
     When used with a localized feedback circuitry, speed performance is increased and bandwidth is extended.

TECHNICAL FIELD OF THE INVENTION

This invention generally relates to electronic systems and in particularto operational amplifier output stages.

BACKGROUND OF THE INVENTION

Operational amplifiers are used in many electronic circuits tocondition, manipulate and amplify signals. The operating characteristicsof a particular operational amplifier are dependent upon its circuittopology. Generally, the operational amplifier consists of a number ofstages, each containing internal sub-stages.

Two important operating characteristics of an operational amplifier areits amplification characteristics and its speed. High beta (β) and highspeed are desirable in operational amplifiers that have a variety ofapplication, including DSL Drivers. Beta (β) refers to the ratio of DCcollector current to DC base current in a bipolar junction transistor orcurrent gain from base to collector. β is very important parameter thatvaries with collector current and temperature.

SUMMARY OF THE INVENTION

The present invention achieves technical advantages as a high β, highspeed operational amplifier output stage using a localized feedbacksystem in which current gains are close to β_(n)*β_(p), where β_(n)refers to the beta of either the pre-driver npn transistor, outputdriver npn transistor or an average of both, depending on the currentsignal and β_(p) refers to the beta of either the pre-driver pnptransistor, output pnp transistor or an average of both. Where signalcurrent is large and positive, load conduction is through the output npntransistor and pre-driver pnp transistor. Where signal current is largeand negative, load conduction is through the pre-driver npn transistorand output pnp transistor. Where the signal is small, load conductionvaries in tandem through the output npn transistor and pre-driver pnptransistor and the output pnp transistor and pre-driver npn transistor.

The output stage can be seen to comprise a pre-driver sub-stage andfinal sub-stage. The pre-driver sub-stage is further comprised of afirst and a second pre-driver sub-stage circuit. In addition, the finalsub-stage is further comprised of a first and a second final sub-stagecircuit. The input to the present invention comprises a transconductance(“g_(n)”) cell which, when a voltage is applied thereto, an errorvoltage appears across the input g_(m) cell and an error current isproduced at the output of the input g_(m) cell. The error current(δI_(in)) flows into the emitters of two pre-driver sub-stagetransistors and flows out of their collectors into the bases of twoother pre-driver transistors. Through this translinear loop, no netsignal is lost. The gained up error currents then flow into the finalsub-stage translinear loop, specifically, into the bases of two finalsub-stage transistors. Effectively, in the small signal context, thefirst pre-driver sub-stage circuit amplifies a positive portion of thecurrent signal for output to the first final sub-stage circuit while thesecond pre-driver sub-stage circuit amplifies a negative portion of thecurrent signal for output to the second final sub-stage circuit. Thefirst and second final sub-stages further amplify the positive portionand negative portion, respectively, of the current signal.

The first and second final sub-stage circuits are interconnected at anoutput terminal of the operational amplifier final stage such that theamplified positive portion of the signal and amplified negative portionof the signal are joined substantially in phase, in the formδI_(o)≈B_(n)*B_(p)*δI_(in). By feeding back a portion of the outputsignal using a variety of feedback principles, speed characteristics canbe further improved.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention, reference ismade to the detailed description taken in conjunction with the followingdrawings:

FIG. 1 is a circuit diagram of a first conventional operationalamplifier output stage;

FIG. 2 is a circuit diagram of a second conventional operationalamplifier output stage;

FIG. 3 is a graph illustrating the linearity characteristics of thefirst conventional operational amplifier. This figure shows the firstderivative (δV_(o)/δV_(i)) of the amplifier's DC transfercharacteristic;

FIG. 4 is a graph illustrating the linearity characteristics of thesecond conventional operational amplifier. This figure shows the firstderivative (δV_(o)/δV_(i)) of the amplifier's DC transfercharacteristic;

FIGS. 5A and 5B show the single ended and differential linearitycharacteristics of the first conventional operational amplifier outputstage using a discrete multi-tone (“DMT”) signal with missing tones;

FIG. 6 is a graph illustrating the typical linearity characteristics ofthe first conventional operational amplifier output stage in harmonicdistortion form;

FIG. 7 is a circuit diagram of a first embodiment of the presentinvention with a g_(m) cell input;

FIG. 8 is a circuit diagram of a second embodiment of the presentinvention with a g_(m) cell input;

FIG. 9 is a graph illustrating the linearity characteristics of thefirst embodiment of the present invention. This figure shows the firstderivative (δV_(o)/δV_(i)) of the amplifier's DC transfercharacteristic;

FIGS. 10A and 10B are graph illustrating the linearity characteristicsof the first embodiment of the present invention using a DMT signal withmissing tones;

FIG. 11 is a graph illustrating the linearity characteristics of thefirst embodiment of the present invention in harmonic distortion form;

FIG. 12 illustrates the translinear loop formed by the first, second,third and fourth transistors;

FIG. 13 illustrates the translinear loop formed by the fifth, sixth,seventh and eight transistors;

FIG. 14 is a circuit diagram of the final sub-stage of the firstembodiment of the present invention using type I biasing of the outputtransistors in a no-load configuration;

FIG. 15 is a circuit diagram of the final sub-stage of the firstembodiment of the present invention using type I biasing of the outputtransistors with a load;

FIG. 16 is a graph illustrating the current gain of the final sub-stageof the first embodiment of the present invention;

FIG. 17 is a circuit diagram of the final sub-stage of the secondembodiment of the present invention using type II biasing of the outputtransistors in a no load configuration;

FIG. 18 is a circuit diagram of the final sub-stage of the secondembodiment of the present invention using type II biasing of the outputtransistors with a signal applied to such final sub-stage's input;

FIG. 19 is a graph illustrating the DC current transfer characteristicof the final sub-stage of FIG. 18;

FIG. 20 is a graph illustrating the DC current transfer characteristicof the final sub-stage of FIG. 15;

FIG. 21 is a graph illustrating the linearity characteristic of thefinal sub-stage of FIG. 15 and FIG. 18. This figure shows the firstderivative (δI_(o)/δI_(i)) of the amplifiers' DC current transfercharacteristics;

FIG. 22 is a circuit diagram of a conventional operational amplifierillustrating bias setup for the output transistors;

FIG. 23 is a graph illustrating the DC current transfer characteristicsof circuit depicted in FIG. 22;

FIG. 24 is a circuit diagram of the first embodiment of the presentinvention with current feedback circuitry;

FIG. 25 is a circuit diagram of the first embodiment of the presentinvention with voltage feedback circuitry;

FIG. 26 is a circuit diagram of the second embodiment of the presentinvention with current feedback;

FIG. 27 is a circuit diagram of the second embodiment of the presentinvention with voltage feedback;

FIGS. 28A, 28B, 28C, 28D, are graph comparing the linearitycharacteristics between the two conventional operational amplifiers andthe first and second embodiments of the present invention. The figureshows the first derivative of the amplifiers' gain.

FIG. 29 is a circuit diagram of the first embodiment of the presentinvention with a compound darlington output stage using type I biasing;

FIG. 30 is a circuit diagram of the first embodiment of the presentinvention with a compound darlington output stage using type I biasingand a differential pair input g_(m) cell;

FIG. 31 is a circuit diagram illustrating a current feedback stabilityloop;

FIG. 32 is a circuit diagram implementing conventional Millercompensation using a current feedback with the embodiments of thepresent invention;

FIG. 33 is a circuit diagram illustrating a voltage feedback stabilityloop;

FIG. 34 is a circuit diagram illustrating implementation of conventionalMiller compensation using voltage feedback to achieve right-half-planezero (“RHPZ”) cancellation with the embodiments of the presentinvention; and

FIG. 35 is a circuit diagram illustrating a method for achieving lowfrequency precision in either of the first or second embodiments of thepresent invention.

DESCRIPTION OF CONVENTIONAL AMPLIFIER OUTPUT STAGES

FIG. 1 is a circuit diagram of a first conventional operationalamplifier output stage. FIG. 2 is a circuit diagram of a secondconventional operational amplifier output stage. FIG. 3 illustrates thelinearity characteristics of such first conventional operationalamplifier by showing the first derivative of the DC transfercharacteristic. FIG. 4 illustrates the linearity of such secondconventional operational amplifier by showing the first derivative offthe DC transfer characteristic. FIG. 5 illustrates the single ended anddifferential linearity of such first conventional operational amplifierwith a discrete multi tone (“DMT”) signal with missing tones. DMT signalis a broadband signal containing many sinusoids spaced at equalintervals. The missing tone performance looks for intermodulationproducts from the broadband DMT signal in at a frequency where there isno sinewave present in the DMT signal. DMT is a rigorous test of anamplifier's linearity. FIG. 6 illustrates the typical linearity of suchfirst and second conventional operational amplifiers in harmonicdistortion form.

DETAILED DESCRIPTION OF THE PRESENT INVENTION

Two embodiments of the present invention are shown in FIGS. 7 and 8. Ascompared to the conventional operational amplifier output stages asdisclosed in FIGS. 1 and 2, the disclosed embodiments of an operationalamplifier output stage as shown in FIGS. 7 and 8, provides a high βoutput (up to β²) and high speed with significantly reduced crossoverdistortion. Because of its high speed, the disclosed invention has theadvantage of extended bandwidth. The disclosed operational amplifieroutput stage comprises a pre-driver sub-stage utilizing translinearcurrent loops and a final sub-stage. The final sub-stage of theoperational amplifier output stage disclosed herein comprises acomplementary set of compound darlington transistors enclosed in alocalized feedback system.

As used herein, translinearity refers to the characteristics ofnon-linear circuits whose operation is based on the exponentialcurrent-voltage relationship of the bipolar junction transistor; βrefers to the ratio of DC collector current to DC base current in abipolar junction transistor or current gain from base to collector; arepresents the fraction of signal current going into one half of thepre-driver sub-stage, λ refers to the fraction of signal current goinginto the other half of the pre-driver sub-stage, and A refers to theemitter area of the BJT in consideration.

FIG. 7 is a circuit diagram of the first embodiment of an operationalamplifier output stage having reduced supply current and high linearityconstructed according to the teachings of the present invention. Thecircuit 100 includes an input g_(m) cell 121, pre-driver sub-stagecomprised of eight pre-driver sub-stage transistors 101, 102, 103, 104,105, 106, 107 and 108, a final sub-stage comprising four final sub-stagetransistors 109, 110, 111 and 112, and four current sources 131, 132,133 and 134. The input g_(m) cell 121 is configured to accept an inputvoltage signal, produce an error voltage across: its input, and producean output error current (δI_(in)).

As shown therein, a first voltage supply rail 41 is coupled to a firstnode 51, a second voltage supply rail 42 is coupled to a fifth node 55.

The first pre-driver sub-stage circuit consists of four transistors 101,102, 103 and 104. In the first pre-driver sub-stage circuit, the emitterof the first transistor 101 is coupled to the first voltage supply rail41 at the first node 51, and the base of the first transistor 101 iscoupled to a second node 52. The emitter of the second transistor 102 isalso coupled to the second node 52; and its base is coupled to a thirdnode 53. The base and collector of the third transistor 103 are alsocoupled to the third node 53. The collector arid base of the fourthtransistor 104 are each coupled to a fourth node 54. The emitter of thefourth transistor 104 is coupled to the voltage supply rail 41 at thefirst node 51.

The second pre-driver sub-stage circuit comprises four transistors 105,106, 107 and 108. The second voltage supply rail 42 is coupled to thefifth node 55. The emitter of the fifth transistor 105 is coupled to thesecond voltage supply rail 42 at the fifth node 55 and its base iscoupled to a the sixth node 56. The emitter of the sixth transistor 106is coupled, to the sixth node 56 and its base is coupled to a seventhnode 57. The collector of the sixth transistor 106 is coupled to thesecond node 52. The base and collector of the seventh transistor 107 arecoupled to a seventh node 57 and its emitter is coupled to an eighthnode 58. The collector and base of the eighth transistor 108 are coupledto the eighth node 58, and the emitter of the eighth transistor 108 iscoupled to the second voltage supply rail 42 at the fifth node 55.

The collector of the second transistor 102 and the emitter of the sixthtransistor 106 are coupled to a common sixth node 56. The emitter of thesecond transistor 102 and the emitter of the sixth transistor 106 arecoupled to a common second node 52. The cross connection advantageouslyresults in no error current being lost in the translinear loops.

A first current source 131 is coupled to the first voltage supply rail41 at the first node 51 and at the second node 52. A second currentsource 132 is coupled to the first voltage supply rail 41 at the firstnode 51 and at the seventh node 57. A third current source 133 iscoupled to the second voltage supply rail 42 at the fifth node 55 and atthe third node 53. A fourth current source 134 is coupled to the voltagesupply rail 42 at the fifth node 55 and at the sixth node 56.

The final sub-stage 123 comprises a complementary pair of darlingtontransistors. The first set of darlington transistors is comprised of theninth and tenth transistors 109 and 110. The emitter of the ninthtransistor 109 is coupled to the collector of the first transistor 101at a ninth node 59. The base and collector of the ninth transistor 109are coupled at a tenth node 60. The base of the tenth transistor 110 iscoupled to the ninth node 59, and the collector of the tenth transistor110 is coupled to the first voltage supply rail 41 at the first node 51.

The second set of darlington transistors is comprised of the eleventhand twelfth transistors 111 and 112. The emitter of the eleventhtransistor 111 is coupled to the collector of the fifth transistor 105at an eleventh node 61. The base and collector of the eleventhtransistor 111 are coupled to the base and collector of the ninthtransistor 109 at the tenth node 60. The base of the twelfth transistor112 is coupled to the eleventh node 61, and the collector of the twelfthtransistor 112 is coupled to the second voltage supply rail 42 at thefifth node 55. The twelfth node 62 couples the emitter of the tenthtransistor 110 to the emitter of the twelfth transistor 112. An outputterminal 91 is coupled to the twelfth node 62. The twelfth node 62 alsointerconnects the output terminal 91 to the g_(m) cell input 121. Theconfiguration of the ninth transistor 109 and eleventh transistor 111 ofthe first embodiment of the present invention is also referred to astype I biasing.

A second embodiment of the present invention is disclosed in FIG. 8. Thesecond embodiment is also referred to as type II biasing of the outputtransistors. In this second embodiment, the collectors of the ninthtransistor 109 and the eleventh transistor 111 are not coupled at thetenth node 60. The collector of the ninth transistor 109 is coupled tothe second voltage supply rail V_(ee) 42 at the fifth node 55 and thecollector of the eleventh transistor 111 is coupled to the first voltagesupply rail V_(cc) 41 at the first node 51. In this case the currentgain from the collectors of 101 or 105 to the output node 91 is theaverage of β_(n) and β_(p). This arrangement minimizes crossoverdistortion in the output signal. As used herein, β_(n) refers to thebeta of transistor 110 and β_(p) refers to the beta of transistor 101,where α=1 and λ=1; or β_(n) refers to the beta of transistor 105 andβ_(p) refers to the beta of transistor 112, where α=0 and λ=0, or, inthe small signal context, where α=0.5 and λ=0.5, β_(n) refers to theaverage of the beta of transistor 110 and transistor 105 and β_(p)refers to the beta of the average of transistor 101 and transistor 112,the relative contribution of each such pnp transistor and npn transistorto β_(n) and β_(p) varying proportionally with the variation in α and β.

FIGS. 9, 10 and 11 illustrate different performance aspects of thepresent invention. Specifically, FIG. 9 shows the linearitycharacteristics of the first embodiment of the present invention,specifically the first derivative (δV_(o)/δV_(i)) of the amplifier's DCtransfer characteristic. FIG. 10 shows the linearity characteristics ofthe first embodiment of the present invention using a DMT signal withmissing tones. FIG. 11 shows the linearity characteristics of the firstembodiment of the present invention in harmonic distortion form.

As shown in FIG. 12, in the first embodiment of the present invention atranslinear loop is formed by the third transistor 103, fourthtransistor 104, second transistor 102 and first transistor 101. Inoperation, two sets of current flow into this first translinear loopwhich sets up a quiescent current through a branch 170 connected at thecollector of the first transistor 101. In addition, as shown in FIG. 13,a translinear loop is formed by the seventh transistor 107, the eighthtransistor 108, the sixth transistor 106 and the fifth transistor 105.Two sets of current flow in this second translinear loop which sets up aquiescent current through a branch 171 connected at a collector of thefifth transistor 105. These two quiescent currents establish the biascurrents for the respective tenth transistor 110 and for the twelfthtransistor 112 by means of translinear principles in the loop formed bythe ninth transistor 109, eleventh transistor 111, tenth transistor 110and twelfth transistor 112.

When an input voltage is applied to the input g_(m) cell 121, an errorvoltage appears across the output of the input g_(m) cell 121 and anerror current is produced. Advantageously, the cross-connection of thecollector of the second transistor 102 to the emitter of the sixthtransistor 106, and the collector of the sixth transistor 106 to theemitter of the second transistor 102 ensures that whatever proportion ofthe error current flowing into the emitters of the second transistor 102and sixth transistor 106 also flows back out through the collectors ofthe second transistor 102 and the sixth transistor 106 into the bases ofthe first transistor 101 and the fifth transistor 105. Advantageously,there is no net signal loss in the pre-driver sub-stage translinearloops.

The error currents into the bases of the first transistor 101 and thefifth transistor 105, are thus gained up by the pre-driver sub-stagecontribution of β_(p) and β_(n) These error currents flow into thetranslinear loop formed by the ninth transistor 109, eleventh transistor111, tenth transistor 110 and twelfth transistor 112. These amplifiederror currents can only flow into the bases of the tenth transistor 110and twelfth transistor 112, where they are amplified by the finalsub-stage contribution of β_(n) and β_(p) respectively. Thus,irrespective of whether the error current flows through the top or thebottom route through the circuit it appears at the output terminal 91amplified by approximately β_(n) multiplied by β_(p), where it developsa correction voltage across the load resistor to move the output to apoint of minimum error of the feedback into the input g_(m) cell 121.

Output Transistor Biasing

FIG. 14 is a circuit diagram of the final sub-stage 123 of the firstembodiment of the operational amplifier output stage in a no loadconfiguration. FIG. 14 illustrates type I biasing of the outputtransistors as follows: Current is flowing into the collector of thetenth transistor 110, referred to as I_(Q110C), and current is flowingout of the collector of the twelfth transistor 112, referred to asI_(Q112C). The emitter area of the ninth transistor 109 is referred toas A_(Q109) and the emitter area of the eleventh transistor 111 isreferred to as A_(Q111). The emitter area of the tenth transistor 110 isreferred to as A_(Q110) and the emitter area the twelfth transistor 112is referred to as A_(Q112). Two current sources I₁₃₅ and I₁₃₆ are shownthereon:$I_{135} = {{I + {\frac{\delta \quad I_{sig}}{2}\quad {and}\quad I_{136}}} = {I - \quad \frac{\delta \quad I_{sig}}{2}}}$

Therefore:$\frac{I_{135}^{2}}{A_{Q109}*A_{Q111}} = \frac{I_{Q110C}*I_{Q112C}}{A_{Q112}*A_{Q110}}$

for β_(n) and β_(p)>>1 and VA_(n) and VA_(p)>>1,

I_(Q110C)=I_(Q112C)=I_(C).

Therefore,${\frac{I_{135}^{2}}{A_{Q109}*A_{Q111}} = \frac{I_{C}^{2}}{A_{Q112}*A_{Q110}}};$

and further$I_{C} = {I_{135} \cdot \sqrt{\frac{A_{Q110}*A_{Q112}}{A_{Q109}*A_{Q111}}}}$

FIG. 15 is a circuit diagram of the final sub-stage 123 of the firstembodiment of the present invention with a load 43. Type I biasing ofthe output transistors is thus described as follows: When a load 43 isconnected to the output terminal 91 and the following do not hold:

β_(n) and β_(p)>>1, or

VA_(n) and VA_(p)>>1, or

there is an imbalance between current I_(Q110C) and I_(Q112C).

Since current I_(Q110C) is not equal to I_(Q112C), an error currentflows in the load 43 thus developing an offset voltage V_(error) acrossthe load 43.

When the difference in current in the final sub-stage transistors 110and 112, are taken care of by a localized feedback system, thecharacteristics of the final sub-stage can be seen as follows: Thesignal current changes the bias currents by increasing the currentthrough the top circuit and decreasing the current through the bottomcircuit. In the limiting case for large current through the top circuitand minuscule current through the bottom circuit, and α is equal to one(1), the translinear loop cuts off the twelfth transistor 112 and all ofthe signal current flows into the base of the tenth transistor 110 whereit appears in the load 43 as follows:

β_(n)*(δI_(sig)).

Conversely, for large signal current through the bottom circuit andminuscule current at the top circuit, and where a is equal to 0, thetranslinear loop is again cut off and all of the signal current flowsinto the base of the twelfth transistor 112 where it appears in the load43 as follows:

β_(p)*(δI_(sig)).

For small signal currents, where a is close to half (0.5), thetranslinear loop is active, that is a quiescent current is flowingthrough both the tenth transistor 110 and the twelfth transistor 112,the signal current splits with α and (1−α) multiplied by δI_(sig)flowing into the base of the twelfth transistor 112. Thus the currentgain from input to output is as follows:

α*β_(n)+(1−α)*β_(p),

for all cases of a such that α is equal to or greater than zero andequal to or less than 1.

As shown in the graph of FIG. 16, the gain will transition from β_(p) toβ_(n) through the translinear region.

FIG. 17 is a circuit diagram of the final sub-stage of the secondembodiment of an operational amplifier in a no load configuration. FIG.17 illustrates type II biasing of the output transistors as follows:${\frac{\beta_{n}*\beta_{p}*i_{b}^{2}}{A_{Q109}*A_{Q111}} = \frac{I_{Q110C}*I_{Q112C}}{A_{Q112} - A_{Q110}}},\quad {and}$$\frac{\beta_{n}*\beta_{p}*i_{b}^{2}}{A_{Q109}*A_{Q111}} = {\frac{\left( {{\beta_{n}*I} - {\beta_{p}*\beta_{n}*i_{b}}} \right)\left( {{\beta \quad I} - {\beta_{n}*\beta_{P}*i_{b}}} \right)}{A_{Q112} - A_{Q110}}.}$

The current through branch 70 is: β_(p)*i_(b).

The current through branch 75 is: I−β_(p)*i_(b).

The current through branch 72 is: β_(n)*i_(b).

The current through branch 74 is: I−β_(n)*i_(b).

The current through branch 76 is: β_(n)*I−β_(p)*β_(n)*i_(b).

The current through branch 77 is: β_(p)*I−β_(n)*β_(p)*i_(b).

As can be seen, an offset current (β_(n)-β_(p))*I will develop an offsetvoltage in a load, and would self correct in the localized feedbackcircuit.

Referring to FIG. 18, which illustrates type II biasing of the outputtransistors:

The current through branch 75 is: I+δI−β_(p)i_(b).

The current through branch 74 is: I+δI−β_(n)i_(b).

The current is through branch 76 is:(β_(n)*I)+(β_(n)*δI)−(β_(n)*β_(p)*i_(b)).

The current through branch 77 is: (β_(p)*I)−(β_(p)*δI)−(β_(n)*β_(p)*δI).

Thus, the output current through branch 78 is:i_(o)=I*(β_(n)−β_(p))+(β_(n)+β_(p))*δI.

This result theoretically indicates no crossover distortion in theoutput, albeit with an offset.

FIGS. 19, 20 and 21 illustrate the-current drive relationships of thetype I and type II biasing schemes.

Pre-Driver Biasing

FIG. 22 is a circuit diagram illustrating one technique of bias currentgeneration for a rail to rail output stage in a conventional operationalamplifier. The main disadvantage of this configuration is that currentgain from the input to the output is only a single β. Also this type ofstage will have a large output impedance making compensation moredifficult given variation in a load's impedance. In the first and secondembodiments of the present invention, translinear principles are used toestablish the bias currents in the pre-driver stage.

Referring back to FIGS. 7 and 8, if there is a slight mismatch in thecurrents through the second transistor 102 and sixth transistor 106 dueto an Early voltage mismatch between these two devices, a cascode on thesecond transistor 102 and the sixth transistor 106 will remedy thiseffect.

Also referring to FIGS. 7 and 8, assume that feedback introduces acorrection term into the circuit to establish equality of collectorcurrents in the first transistor 101 and the fifth transistor 105, then:

 I_(Q101C)=I_(Q105C)=I_(Qpre)

Thus, from translinear principles:${{1.\quad \frac{I_{132}^{2}}{A_{Q107}*A_{Q108}}} = {\frac{I_{Q106C}}{A_{Q106}}*\frac{I_{Qpre}}{A_{Qpre}}}};$${{2.\quad \frac{I_{132}^{2}}{A_{Q103}*A_{Q104}}} = {\frac{I_{Q102C}}{A_{Q102}}*\frac{I_{Qpre}}{A_{Qpre}}}};$

 I_(Q106C)=I_(Q102C)=I₁₃₁;  3.

${{4.\quad \frac{I_{132}^{2}}{A_{Q107}*A_{Q108}}} = {{\frac{A_{Q101}}{I_{Q_{pre}C}}*A_{Q106}} = I_{Q106C}}};$

(derived from equation 1);${{5.\quad \frac{I_{132}^{2}}{A_{Q103}*A_{Q104}}} = {{\frac{I_{Q105}}{A_{Q_{pre}C}}*A_{Q102}} = I_{Q102C}}};$

(derived from equation 2);${{{6.\quad \frac{I_{132}^{2}}{A_{Q107}*A_{Q108}}*\frac{I_{Q105}}{A_{Q_{pre}C}}*A_{Q106}} + {\frac{I_{132}^{2}}{A_{Q103}*A_{Q104}}*\frac{A_{Q101}}{I_{Q_{pre}C}}*A_{Q102}}} = I_{131}};$${Thus},\quad {I_{Q_{pre}C} = {\frac{I_{132}^{2}}{I_{131}}{\left( {\frac{A_{Q105}*A_{Q106}}{A_{Q107}*A_{Q108}} + \frac{A_{Q101}*A_{Q102}}{A_{Q103}*A_{Q104}}} \right).}}}$

(derived from equations 3, 4 and 5)

Referring to the operational amplifier output stage 100 shown in FIG. 7,the change in current in the first transistor 101 and the fifthtransistor 105 in response to a change in input current is computed asfollows: The input current change takes the form of an equal butopposite change in I_(X) and I_(Y) given that the difference currentbetween I_(X) and I_(Y) (i.e. δI) has to be divided between the bases ofthe first transistor 101 and the fifth transistor 105. Therefore,

I _(o) =I _(Y) −α*δI*β _(p) I _(Y)−(1−α)δI−β _(n)

δI _(o) =−*αδI*β _(p)−(1−α)δI*β _(n);

δI _(o) =−δI(α*β_(p)+(1−α)−β_(n)).

Where α a is greater than zero and less than one, the value of αindicates the proportion of δI delivered into the bases of each of thepre-driver transistors, first transistor 101 and fifth transistor 105.

Where a is approximately zero, I_(X) has significantly increased andI_(Y) has significantly decreased by equal and opposite quantities. Thebase-emitter voltage is large in the second transistor 102 and small inthe sixth transistor 106. The second transistor 102 cuts off and all ofthe difference current between I_(X) and I_(Y) (i.e. δ1) flows into thebase of the fifth transistor 105. This gives a current gain in thecircuit of β_(n).

Where α is approximately equal to one, the opposite of where α isapproximately equal to zero occurs. Where I_(X) significantly decreases,I_(Y) significantly increases causing all difference current, δI, toflow into base of the first transistor 101, resulting in a current gainof β_(p).

Where α is greater than zero but less than one, the pre-driver sub-stage122 is in translinear mode. The difference current is split in varyingproportion into the first transistor 101 and the fifth transistor 105.Thus, δI_(o)/δI=α*β_(p)+(1−α)*β_(n).

Referring to FIG. 23, the DC response of the pre-driver sub-stage 122 ofthe present invention is shown.

In connection with the coupling of the pre-driver sub-stage 122 to thefinal sub-stage 123, the biasing scheme of the pre-drivers and thebiasing scheme of the final drivers of the present invention have theadvantageous property of not absorbing any signal current. All of thesignal current is delivered directly into the bases of the transistors,and none is lost in translinear loops.

The current gain from the input to the output has approximately theform:

δI _(o)≈β_(n)*β_(p) *∂I _(in).

Feedback Analysis

When feedback is locally applied by means of some localized feedbackcircuit, the errors are corrected within a very tight loop which willrespond much more quickly than relying on the amplifier overall feedbackloop. This localized feedback provides the present invention with highspeed capabilities.

Four (4) possibilities are presented: (i) current feedback, transitionalβ output (ii) current feedback, constant β output (iii) voltagefeedback, transitional β output, and (iv) voltage feedback, constant βoutput.

FIG. 24 is a circuit diagram of a first embodiment of the presentinvention with a current feedback circuitry. FIG. 25 is a circuitdiagram of the first embodiment of the present invention with a voltagefeedback circuitry.

When the input g_(m) cell 121 takes the form of a complementarydifferential pair, the inherent RHPZ appearing when the pre-driversub-stage is Miller compensated vanishes as the feed forward termcontributing to the RHPZ is pulled back out by the differential pair.

FIG. 28 illustrates the output in a closed loop configuration with[greater than unity gain] driving a heavy load over a wide voltagerange. In all cases the worst case non-linearity is approximatelyplus/minus 1 part in 1000. For the current feedback, constant β output,cross-over distortion is virtually eliminated.

FIG. 29 is a circuit diagram of the first embodiment of the presentinvention with a compound darlington output stage using type I biasing.A generalized evaluation of this circuit is as follows:

Referring to current through branches 150, 152, 154 156, 158, 160, 172and 174 in FIG. 29:

Current through branch 150 is I_(LTP); where I_(LTP) refers to thecurrent through current source 131.

Current through branch 152 is: −α·δI.

Current through branch 154 is:$\frac{I_{LTP}}{2} + {\delta \quad {{I\left( {\frac{1}{2} - \alpha} \right)}.}}$

Current through branch 156 is:$\frac{I_{LTP}}{2} - \quad {\frac{\delta \quad I}{2}.}$

Current through branch 158 is:$\frac{I_{LTP}}{2} + {\frac{\delta \quad I}{2}.}$

Current through branch 160 is: I_(biasp)−β_(Q101)·α·δI.

Current through branch 162 is approximately equal to:$I_{biasp} - \quad \frac{I_{LTP}}{2} - {\delta \quad {I \cdot \beta_{Q101} \cdot {\alpha.}}}$

Current through 172 is: −λ·δI(β_(Q101)·α+β_(Q105)(1−α)).

Current through 174 is: −λ·δI·(β_(Q101)·α+β_(Q105)(1−α))+I_(bias out).

Referring to current through branches 151, 153, 155, 157, 159, 161, 163,173 and 175:

Current through branch 151 is I_(LTP); where I_(LTP) refers to thecurrent through current source 134 which is the same as the currentthrough current source 131.

Current through branch 153 is: (1−α)δI

Current through branch 155 is:$\frac{I_{LTP}}{2} + {\delta \quad {{I\left( {\frac{1}{2} - \alpha} \right)}.}}$

Current through branch 157 is:$\frac{I_{LTP}}{2} + {\frac{\delta \quad I}{2}.}$

Current through branch 159 is:$\frac{I_{LTP}}{2} - \quad {\frac{\delta \quad I}{2}.}$

Current through branch 161 is: I_(bias p)+β_(Q105)·(1−α)δI.

Current through branch 163 is:$I_{biasp} - \quad \frac{I_{LTP}}{2} + {{\beta_{Q105} \cdot \left( {1 - \alpha} \right)}\delta \quad {I.}}$

Current through branch 173 is: (1−λ)·δI(β_(Q101)·α+β_(Q105)(1−α).

Current through 175 is: (1−λ)−δI(β_(Q101)·α+β_(Q105)(1−α)+I_(bias out).

Therefore:

I_(out)=−λ•δI•β_(Q110)• (β_(Q101)•α+β_(Q105) (1−α))−)1−λ)•δI•β_(Q112)(β_(Q101)•α+β_(Q105)(1−α)).

In a first case where I_(out) is large and positive, and load conductionis through transistor 110 and transistor 101, where α=1, λ=1, then:

I _(out) =−δI·β _(Q110)·β_(Q101)

In a second case where lout is large and negative, and load conductionis through transistor 112 and transistor 105, where α=0, λ=0, then:

I _(out) =−δI·β _(Q112)·β_(Q105)

In a third case where I_(out) is very small through the cross-overpoint, and load conduction is through transistor 110 and transistor 112,where α≈0.5, λ≈0.5, then:$I_{out} = {{- \delta}\quad {I\left( \frac{\beta_{Q101} + \beta_{Q105}}{2} \right)}\left( \frac{\beta_{110} + \beta_{112}}{2} \right)}$

Thus, for β_(Q112)=β_(Q101)=β_(p)

and β_(Q110)=β_(Q105)=β_(n)$I_{out} = {{- \delta}\quad {I\left( \frac{\beta_{p} + \beta_{n}}{2} \right)}^{2}}$

FIG. 30 is a circuit diagram of the first embodiment of the presentinvention with a compound darlington output stage using type I biasingand a differential pair input g_(m) cell. A specific evaluation of thiscircuit is as follows:

Referring to the current through branches 140, 142, 152, 160, 172 and174 in FIG. 30:

The current through branch 140 is:

I ₁₃₁ +δI(½−α)

The current through branch 142 is: $- \quad \frac{\delta \quad I}{2}$

The current through branches 152, 160, 172 and 174 are the same as thatin the equivalent numbered branches in FIG. 29.

Referring to the current through branches 141, 143, 153, 161, 173, and175 in FIG. 30:

The current through branch 141 is:

I ₁₃₄ +δI(½−α)

The current through branch 143 is: $\frac{\delta \quad I}{2}$

The current through branches 153, 161, 173 and 175 are the same as thatin the equivalent numbered branches in FIG. 29.

Therefore:

I _(out) =−λ·δI·β _(Q110)·(β_(Q101)·α+β_(Q105)(1−α))−(1−λ)·δI_(Q112)(β_(Q101)·α+β_(Q105)(1−α)).

Referring to FIG. 30, and as noted in FIG. 29, in a first case, whereI_(out) is large and positive, and load conduction is through transistor110 and transistor 101, where α=1, λ=1, then:

I _(out) =−δI·β _(Q110)·β_(Q101)

In a second case where I_(out) is large and negative, and loadconduction is through transistor 112 and transistor 105, where α=0, λ=0,then:

I _(out) =−δI·β _(Q112)·β_(Q105)

In a third case, where case I_(out) is very small through the cross-overpoint, and load conduction is through transistor 110 and transistor 112,where α≈0.5, λ≈0.5, then:$I_{out} = {{- \delta}\quad {I\left( \frac{\beta_{Q101} + \beta_{Q105}}{2} \right)}\left( \frac{\beta_{Q110} + \beta_{Q112}}{2} \right)}$

Thus, for β_(Q112)=β_(Q101)=β_(p)

and β_(Q110)=β_(Q105)=β_(n)$I_{out} = {{- \delta}\quad {I\left( \frac{\beta_{p} + \beta_{n}}{2} \right)}^{2}}$

where 0<α<1;

and 0<λ<1

I_(biasp) and I_(biasout) are established using translinear principles.

Compensation

FIGS. 31, 32, 33 and 34 show the various types of compensationtechniques that can be used with the present invention. FIG. 31 is ahalf circuit showing the current feedback case with small signal AC. Thecircuit is a 2 voltage gain stage amplifier with voltage gain beingdeveloped at nodes 63 and 64. The circuit lends itself to classic Millercompensation as shown in FIG. 31.

Referring to FIG. 32, the resistor 81 eliminates the right half planethrough the compensation capacitor 85. At the quiescent condition, thevalue is the reciprocal of the transconductance of the first transistor101.

FIG. 33 illustrates the voltage feedback case. Referring to the circuitin FIG. 33, there are two (2) loops to be compensated, inner loop 2 andouter loop 1. As can be seen in FIG. 32, similar to the current feedbackimplementation, the system is a 2 voltage gain stage amplifier withvoltage gain at nodes 63 and 64. This circuit can also be Millercompensated. There is no concern with RHPZ because the differentialtransistor 113 draws the feed forward signal out.

Implementation

It is noted that the voltage feedback implementation can only be usedfor gain greater than 1. Further, the current feedback implementationcan be used for if arbitrary gain. All four implementations can be usedas a stand alone amplifier configuration.

FIG. 35 illustrates how gain from the present invention can be preservedwhere additional lower frequency precision is required.

The advantages of the present invention over conventional operationalamplifier output stages is significantly higher linearity for the samesupply current or linearity equal to the conventional operationalamplifiers.

The current gain obtained in the error correction loop of each of thefirst and second conventional operational amplifiers is only a singlecurrent gain whereas the current gain of the present invention is up toβ². Further, the DC non-linearity of conventional amplifiers isapproximately 2 parts per 1000, a factor of 25 worse than the presentinvention. Reduced current draw is one of the advantages afforded by thedesign of each of the present invention.

The numerous innovative teachings of the present application aredescribed with particular reference to the disclosed embodiments.However, it should be understood that these embodiments provide only twoexamples of the many advantageous uses and innovative teachings herein.Various alterations, modifications and substitutions can be made to thedisclosed invention without departing in any way from the spirit andscope of the invention, as defined in the claims that follow. Forexample, although the embodiments have been presented herein withreference to particular transistor types, voltage and current polaritiesand methods of coupling, the present inventive structures andcharacteristics are not necessarily limited to particular transistortypes, polarities or methods of coupling, as used herein. It should beunderstood the embodiment used hereinabove can easily be implementedusing many diverse transistor types, polarities and methods of couplingso long as the combinations achieve a high beta, high speed operationalamplifier output stage with reduced current draw and extended bandwidth.

What is claimed is:
 1. An operational amplifier output stage,comprising: a pre-driver sub-stage and a final sub-stage, the pre-driversub-stage having a plurality of transistors being biased by a pluralityof current sources, the pre-driver sub-stage being adapted to accept acurrent signal (δI_(in)) from an input g_(m) cell; the pre-driver stagebeing further adapted to provide biasing to a plurality of transistorsin the final sub-stage; and the pre-driver sub-stage being coupled tothe final sub-stage so as to provide current gain from input to outputof δI_(o)≈β_(n)*β_(p)*δI_(in); and localized feedback circuitry enclosedin the output stage operable to correct signal errors more rapidly thanan overall amplifier feedback loop, thereby improving the speedcharacteristics of the operational amplification output stage.
 2. Theoperational amplifier output stage recited in claim 1, furthercomprising inherent RHPZ cancellation operable to extend bandwidth. 3.The operational amplifier output stage recited in claim 1, wherein theplurality of transistors in the final sub-stage comprises 4 transistorsarranged as a complementary pair of differential transistors enclosed ina localized feedback system.
 4. The operational amplifier output stagerecited in claim 1 for use in an integrated circuit.
 5. The operationalamplifier output stage recited in claim 1 for use in a DSL driver.